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Algorithms for superiorization and their applications to image reconstruction.

机译：优势算法及其在图像重建中的应用。

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摘要

Computational tractability with limited computing resources is a major barrier for the ever increasing problem sizes of constrained optimization models that seek a minimum of an objective function satisfying a set of constraints. On the other hand, there exist efficient and computationally much less demanding iterative methods for finding a feasible solution that only fulfills the constraints. These methods can handle problem sizes beyond which existing optimization algorithms cannot function. To bridge this gap we present a new concept called superiorization, envisioned methodologically as lying between optimization and feasibility seeking. It enables us to use efficient iterative methods to steer the iterates toward a point that is feasible and superior, but not necessarily optimal, with respect to the given objective/merit function.;Using efficient iterative methods to do 'superiorization' instead of 'full constrained optimization' or only 'feasibility' is a new tool for handling mathematical models that include constraints and a merit function. The target improvement of the superiorization methodology is to affect the computational treatment of the mathematical models so that we can reach solutions that are desirable from the point of view of the application at hand at a relatively small computational cost. The key to superiorization is our discovery that two principal prototypical algorithmic schemes, string-averaging projections and block-iterative projections, which include many projection methods, are bounded perturbation resilient. While stability of algorithms under perturbations is usually made to cope with all kinds of imperfections in the data, here we have taken a proactive approach designed to extract specific benefits from the kind of stability that we term perturbation-resilience. Superiorization uses perturbations proactively to reach feasible points that are superior, according to some criterion, to the ones to which we would get without employing perturbations. In this work, we set forth the fundamental principle of the superiorization methodology, give some mathematical formulations, theorems and results, and show potential benefits in the field of image reconstruction from projections.
机译：具有有限计算资源的可计算可处理性是约束优化模型的问题规模不断增大的主要障碍，该模型要求寻求满足一组约束的最小目标函数。另一方面，存在用于找到仅满足约束条件的可行解决方案的有效且计算上要求较少的迭代方法。这些方法可以处理现有的优化算法无法解决的问题规模。为了弥合这种差距，我们提出了一种称为“优势”的新概念，该概念在方法上被设想为处于优化和可行性寻求之间。它使我们能够使用有效的迭代方法将迭代引导到相对于给定的目标/优点函数而言可行且优越的点，但不一定是最优的点;使用有效的迭代方法进行``超级化''而不是``完全化''约束优化”或仅“可行性”是用于处理包含约束和绩效函数的数学模型的新工具。优越性方法的目标改进是影响数学模型的计算处理，以便我们可以以相对较小的计算成本从手头的应用程序角度获得理想的解决方案。优越性的关键在于我们发现两个主要的原型算法方案，包括许多投影方法的字符串平均投影和块迭代投影，具有有限的摄动弹性。虽然通常使扰动下的算法稳定性来应对数据中的各种缺陷，但在这里，我们采取了一种主动的方法，旨在从我们称为扰动弹性的那种稳定性中提取特定的好处。优越性主动使用扰动来达到可行的点，根据某些标准，这些点要优于不采用扰动所能达到的点。在这项工作中，我们阐述了优越性方法的基本原理，给出了一些数学公式，定理和结果，并显示了在基于投影的图像重建领域中的潜在利益。

著录项

  • 作者

    Davidi, Ran.;

  • 作者单位

    City University of New York.;

  • 授予单位 City University of New York.;
  • 学科 Computer Science.
  • 学位 Ph.D.
  • 年度 2010
  • 页码 122 p.
  • 总页数 122
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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